13-odd-limit: Difference between revisions

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This is a list of 13-odd-limit intervals. To [[11-odd-limit]], it adds 5 additional interval pairs.
{{Odd-limit navigation|13}}
{{Odd-limit intro|13}}


<ul><li>[[14/13|14/13]], [[13/7|13/7]]</li><li>[[13/12|13/12]], [[24/13|24/13]]</li><li>[[12/11|12/11]], [[11/6|11/6]]</li><li>[[11/10|11/10]], [[20/11|20/11]]</li><li>[[10/9|10/9]], [[9/5|9/5]]</li><li>[[9/8|9/8]], [[16/9|16/9]]</li><li>[[8/7|8/7]], [[7/4|7/4]]</li><li>[[7/6|7/6]], [[12/7|12/7]]</li><li>[[13/11|13/11]], [[22/13|22/13]]</li><li>[[6/5|6/5]], [[5/3|5/3]]</li><li>[[11/9|11/9]], [[18/11|18/11]]</li><li>[[16/13|16/13]], [[13/8|13/8]]</li><li>[[5/4|5/4]], [[8/5|8/5]]</li><li>[[14/11|14/11]], [[11/7|11/7]]</li><li>[[9/7|9/7]], [[14/9|14/9]]</li><li>[[13/10|13/10]], [[20/13|20/13]]</li><li>[[4/3|4/3]], [[3/2|3/2]]</li><li>[[11/8|11/8]], [[16/11|16/11]]</li><li>[[18/13|18/13]], [[13/9|13/9]]</li><li>[[7/5|7/5]], [[10/7|10/7]]</li></ul>
* [[1/1]]
[[Category:just_interval]]
* '''[[14/13]], [[13/7]]'''
* '''[[13/12]], [[24/13]]'''
* [[12/11]], [[11/6]]
* [[11/10]], [[20/11]]
* [[10/9]], [[9/5]]
* [[9/8]], [[16/9]]
* [[8/7]], [[7/4]]
* [[7/6]], [[12/7]]
* '''[[13/11]], [[22/13]]'''
* [[6/5]], [[5/3]]
* [[11/9]], [[18/11]]
* '''[[16/13]], [[13/8]]'''
* [[5/4]], [[8/5]]
* [[14/11]], [[11/7]]
* [[9/7]], [[14/9]]
* '''[[13/10]], [[20/13]]'''
* [[4/3]], [[3/2]]
* [[11/8]], [[16/11]]
* '''[[18/13]], [[13/9]]'''
* [[7/5]], [[10/7]]
 
{| class="wikitable center-all right-2 left-5"
! Ratio
! Size ([[cents|¢]])
! colspan="2" | [[Color name]]
! Name(s)
|-
| [[14/13]]
| 128.298
| 3uz2
| thuzo 2nd
| tridecimal large semitone
|-
| [[13/12]]
| 138.573
| 3o2
| tho 2nd
| tridecimal supraminor second / tridecimal subneutral second
|-
| [[13/11]]
| 289.210
| 3o1u3
| tholu 3rd
| tridecimal minor third
|-
| [[16/13]]
| 359.472
| 3u3
| thu 3rd
| tridecimal supra-neutral third
|-
| [[13/10]]
| 454.214
| 3og4
| thogu 4th
| tridecimal subfourth / tridecimal third-fourth
|-
| [[18/13]]
| 563.382
| 3u4
| thu 4th
| tridecimal superfourth
|-
| [[13/9]]
| 636.618
| 3o5
| tho 5th
| tridecimal subfifth
|-
| [[20/13]]
| 745.786
| 3uy5
| thuyo 5th
| tridecimal superfifth / tridecimal fifth-sixth
|-
| [[13/8]]
| 840.528
| 3o6
| tho 6th
| tridecimal subneutral sixth
|-
| [[22/13]]
| 910.790
| 3u1o6
| thulo 6th
| tridecimal major sixth
|-
| [[24/13]]
| 1061.427
| 3u7
| thu 7th
| tridecimal supra-neutral seventh
|-
| [[13/7]]
| 1071.702
| 3or7
| thoru 7th
| tridecimal submajor seventh
|}
The smallest [[equal division of the octave]] which is [[consistent]] in the 13-odd-limit is [[26edo]].
 
<span data-darkreader-inline-color="">The smallest one which is distinctly consistent in the same is</span> [[87edo]].
 
== See also ==
* [[13-limit]] ([[prime limit]])
* [[Diamond13]] – as a scale
 
[[Category:13-odd-limit| ]] <!-- main article -->

Latest revision as of 13:42, 8 October 2025

← 11-odd-limit  13-odd-limit  15-odd-limit →

The 13-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 13 and k is an integer. To the 11-odd-limit, it adds 6 pairs of octave-reduced intervals involving 13.

Below is a list of all octave-reduced intervals in the 13-odd-limit.

Ratio Size (¢) Color name Name(s)
14/13 128.298 3uz2 thuzo 2nd tridecimal large semitone
13/12 138.573 3o2 tho 2nd tridecimal supraminor second / tridecimal subneutral second
13/11 289.210 3o1u3 tholu 3rd tridecimal minor third
16/13 359.472 3u3 thu 3rd tridecimal supra-neutral third
13/10 454.214 3og4 thogu 4th tridecimal subfourth / tridecimal third-fourth
18/13 563.382 3u4 thu 4th tridecimal superfourth
13/9 636.618 3o5 tho 5th tridecimal subfifth
20/13 745.786 3uy5 thuyo 5th tridecimal superfifth / tridecimal fifth-sixth
13/8 840.528 3o6 tho 6th tridecimal subneutral sixth
22/13 910.790 3u1o6 thulo 6th tridecimal major sixth
24/13 1061.427 3u7 thu 7th tridecimal supra-neutral seventh
13/7 1071.702 3or7 thoru 7th tridecimal submajor seventh

The smallest equal division of the octave which is consistent in the 13-odd-limit is 26edo.

The smallest one which is distinctly consistent in the same is 87edo.

See also

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